Phase Velocity Dispersion and Attenuation of Seismic Waves due to Trapped Fluids in Residual Saturated Porous Media

Abstract

Propaga on of seismic waves in par ally saturated porous media depends on various material proper es, including satura on, porosity, elas c proper es of the skeleton, viscous proper es of the pore fl uids, and, addi onally, capillary pressure and eff ec ve permeability. If the we ng fl uid is in a discon nuous state (i.e., residual saturated confi gura on), phase veloci es and frequency-dependent a enua on addi onally depend on microscopical (pore-scale) proper es such as droplet and/or ganglia size. To model wave propaga on in residual saturated porous media, we developed a three-phase model based on an enriched con nuum mixture theory capturing the strong coupling between the micro-and the macroscale. The three-phase model considers a con nuous and a discon nuous part. The con nuous part exhibits similar behavior as the poroelas c model introduced by Biot. The discon nuous part describes the movement of blobs/clusters of the we ng fl uid and is based on an oscillator rheology. In comparison with other three-phase models, the presented one accounts for the heterogeneity of the discon nuous fl uid clusters by use of their dynamic proper es, i.e., their sta s cally distributed iner a, eigenfrequency, and damping eff ects. This heterogeneous and discon nuous distribu on of the we ng fl uid in the form of single blobs or fl uid clusters is represented by a model-embedded distribu on func on of the cluster sizes. We defi ne a dimensionless parameter that determines if the overall mo on of the residual fl uid is dominated by oscilla ons (underdamped, resonance) or not (overdamped). Our results show that the residual fl uid has a signifi cant impact on the velocity dispersion and a enua on no ma er if it oscillates or not. For long wavelengths our model coincides with the Biot-Gassmann equa ons. We show under which condi ons and how the classical biphasic models can be used to approximate the dynamic behavior of residual saturated porous media.Abbrevia ons: PDF, probability density func on; REV, representa ve elementary volume.To understand and characterize the dynamical behavior of partially saturated porous media, such as soils, rocks, or organic materials, the partial properties of the solid skeleton, of the inherent pore fl uids and, in addition, the main physical coupling eff ects between these interacting constituents have to be taken into account. Since the seminal work of Biot (1956a,b) and Frenkel (1944) in the middle of the last century, many theoretical and numerical studies about wave propagation phenomena in fully saturated porous media have been published (e.g., Bourbié et al., 1987;Stoll, 1989;Carcione, 2007, and references therein). To describe the macroscopic behavior of seismic waves propagating through partially saturated media (i.e., porous media saturated with a wetting and a nonwetting pore fl uid), the biphasic Biot-type approach was extended to take into account quasistatic (Santos et al., 1990;Tuncay and Corapcioglu, 1996;Wei and Muraleetharan, 2002;Carcione et al., 2004;Lo and Sposito, 2005;...

Krauklis wave initiation in fluid-filled fractures by seismic body waves

“…Therefore, Krauklis wave effects in a rock with a narrow distribution of fracture lengths should lead to a strongly frequency-dependent wave propagation behavior for body waves, as Korneev (2008) speculates. On the other hand, if the resonance frequencies are widely distributed, the model of Steeb et al (2012) predicts that the rock's dispersion behavior stays the same, but the peak dispersion and attenuation are shifted to higher frequencies. Therefore, Krauklis wave effects in a rock with strongly varying fracture lengths should not lead to such a pronounced frequency dependency for body-wave propagation, but the dependency on fracture orientation may still remain.…”

“…The above-mentioned effective medium models (Frehner et al, 2009Huang et al, 2009;Steeb et al, 2010Steeb et al, , 2012, incorporating a rock-internal oscillatory behavior into wave propagation models, are isotropic. However, Figures 6 and 7 demonstrate that Krauklis wave initiation strongly depends on fracture orientation, reflecting an anisotropy effect.…”

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

“…From this information, one could calculate, for example, the distribution of trapped cluster sizes (Iglauer et al, 2011) or the distribution of the wetting angle as a function of pore shape and size. The residual cluster size distribution can be related to an eigenfrequency distribution of these clusters, which can modify the acoustic response of the bulk rock (Frehner et al, 2010;Steeb et al, 2012). • The images can also be used for studying acoustic wave attenuation based on the distribution of viscous fluids and the geometry and distribution of pores.…”

Frequency‐dependent properties of multiphase materials: origins, needs, and effective use in geophysics and modern synthetic materials.

“…[4] for detailed analysis and formulas. Moreover, fluid-fluid interfaces play an extra role in the case of partially and residually saturated porous media [9]. They determine capillary pressure and resonance effects of enclosed fluid conglomerations [2,3].…”

“…In all cases, an accurate description is of vital importance for reliable predictions and interpretation. For example, changing flow profiles can lead to modified attenuation regimes and multiple oscillations modes yield distinct stimulation regimes of enclosed fluid clusters [6,9]. Moreover, wrong assumptions can lead to errors of several hundred percent when estimating characteristic frequencies, for instance, in the case of osteoporotic bone or high-porosity foams [4].…”